Properties of G-martingales with finite variation and the application to G-Sobolev spaces

As is known, if $B={\left(B_t\right)}_{t\in [0,T]}$ is a $G$-Brownian motion, a process of form ${\int }_0^t{\eta }_{s}d{〈B〉}_s?{\int }_0^{t}2G\left({\eta }_s\right)ds$, $\eta \in M_G^1(0,T)$, is a non-increasing $G$-martingale. In this paper, we shall show that a non-increasing $G$-martingale cannot be form of ${\int }_0^t{\eta }_{s}ds$ or ${\int }_0^t{\gamma }_{s}d{〈B〉}_s$, $\eta ,\gamma \in M_G^1(0,T)$, which implies that the decomposition for generalized $G$-Itô processes is unique: For arbitrary $\zeta \in H_G^1(0,T)$, $\eta \in M_G^1(0,T)$ and non-increasing $G$-martingales $K,L$, if ${\int }_0^t{\zeta }_{s}d{B}_s+{\int }_0^t{\eta }_{s}ds+K_t=L_t,t\in [0,T],$then we have $\eta \equiv 0$, $\zeta \equiv 0$ and$K_t=L_t$. As an application, we give a characterization to the $G$-Sobolev spaces introduced in Peng and Song (2015).     

Two-component generalized Ragnisco–Tu equation and the Riemann–Hilbert problem

Theoretical and Mathematical Physics - Using the Riemann–Hilbert approach, we investigate the two-component generalized Ragnisco–Tu equation. The modified equation is integrable in the...     

Joint optimization of channel allocation and power control for cognitive radio networks with multiple constraints

Wireless Networks - With the increasing demands for wireless communication, efficiently using the spectrum resource has always been an important research topic. In this paper, the problem of N...     

Effectively promoted catalytic activity by adjusting calcination temperature of Ce-Fe-Ox catalyst for NH3-SCR

A series of Ce-Fe-O_x catalysts prepared by the different calcination temperatures (marked as CF-X, where X represented calcination temperature) were used to the selectivity catalytic reduction of NO_x by NH₃. The results explained the relationship between calcination temperature and the sulfate species over Ce-Fe-O_x, and then investigated the surface acidity and catalytic performance. The large amounts of sulfate species were formed over CF-450 and CF-550 while it was decomposed with further the increasing of calcination temperature, which resulted in the loss of surface acidity, causing a decrease in the catalytic activity over Ce-Fe-O_x. Thereby, the CF-450 catalyst showed the best catalytic activity and over 90% NO_x conversion was obtained at 244–450 °C. Besides, the favored pore structure, more Fe³⁺ active species, higher Ce³⁺ concentration and the abundance of chemical adsorbed oxygen species, as well as the surface acid sites, would together contribute to the excellent catalytic activity of CF-450 catalyst.     

Metal–Organic Framework (MOF)-Derived Carbon-Mediated Interfacial Reaction for the Synthesis of CeO2−MnO2 Catalysts

CeO₂-based catalysts are widely studied in catalysis fields. Developing one novel synthetic approach to increase the intimate contact between CeO₂ and secondary species is of particular importance for enhancing catalytic activities. Herein, an interfacial reaction between metal–organic framework (MOF)-derived carbon and KMnO₄ to synthesize CeO₂−MnO₂, in which carbon is derived from the pyrolysis of Ce-MOFs under an inert atmosphere, is described. The MOF-derived carbon is found to restrain the growth of CeO₂ crystallites under a high calcination temperature and, more importantly, intimate contact within CeO₂/C is conveyed to CeO₂/MnO₂ after the interfacial reaction; this is responsible for the high catalytic activity of CeO₂−MnO₂ towards CO oxidation.     

Efficient Syntheses of Traumatic Lactone and Rhizobialide

Herein, we report the total synthesis of traumatic lactone and rhizobialide by utilizing allenoic acid to construct the lactone ring. The key starting materials, allenoic acids, could be prepared by the ATA (allenation of terminal alkynes) of a terminal alkyne with an aldehyde that contained a protected hydroxyl group followed by hydrolysis. Importantly, the asymmetric synthesis could be realized just by replacing racemic diphenylprinol with (R)- or (S)-diphenylprinol to deliver the optically active allenoate.     

Mechanism of Catalytic Effect of Water Clusters on the Oxidation of Phosphine Gas

Russian Journal of Physical Chemistry A - The mechanism of PH3 oxidation is investigated at B3LYP/6-311+g (d, p) level using density functional theory calculation with n = 0–6 water molecules...     

Impact of post-injection strategy on the physicochemical properties and reactivity of diesel in-cylinder soot

Post injection has significant benefit in the reduction of diesel soot emissions. Therefore, there is a need to understand the effect of post-injection strategy on soot physicochemical properties and reactivity because they play an important role in soot oxidation process that governs the final soot emissions. This work focuses on the impact of post injection on the physicochemical properties and reactivity of diesel in-cylinder soot using a main plus post injection (M*P) and a single injection (M) strategy. The soot was sampled by a developed total cylinder sampling system, and the dividing points of soot formation-dominant and oxidation-dominant phases were used for studying the impacts of post injection on the characteristics of in-cylinder soot. The physicochemical properties of the soot samples, including primary particle size, nanostructure, carbon chemical state and surface functional groups, were characterized. The soot reactivity was evaluated in terms of peak temperature, burnout temperature and apparent activation energy. In the oxidation-dominant phase, the M*P soot initially possesses smaller primary particle size, shorter fringe length, larger tortuosity, lower sp²/sp³ hybridization ratio of carbon atoms and higher content of aliphatic CH groups than the M soot. The beneficial influence of physicochemical properties on soot reactivity when using post injection is validated by the thermogravimetric data, which shows that the M*P soot is more reactive than the M soot at the onset of the oxidation-dominant phase. In the M*P case, the soot generated from the main-injection combustion has lower reactivity than the soot from the post-injection combustion after they experience the soot formation-dominant phase. The results indicate that the use of post injection leads to in-cylinder soot with physicochemical properties that favor reactivity. The enhancement of reactivity means that the soot will be more readily oxidized in the subsequent combustion process, and consequently contributes to a reduction in final soot emissions.